Print all root to leaf paths with there relative positions

Print all root to leaf paths with there relative positions

Given a binary tree, print the root to the leaf path, but add “_” to indicate the relative position.

Input : Root of below tree
         A 
       /   \  
      B      C 
     / \    / \
    D   E   F  G

Output : All root to leaf paths
_ _ A
_ B
D

_ A
B
_ E

 A
 _ C
 F

A
_ C
_ _ G

The idea base on print path in vertical order.

Below is complete algorithm :

1) We do Preorder traversal of the given Binary Tree. While traversing the tree, we can recursively calculate horizontal distances or HDs. We initially pass the horizontal distance as 0 for root. For left subtree, we pass the Horizontal Distance as Horizontal distance of root minus 1. For right subtree, we pass the Horizontal Distance as Horizontal Distance of root plus 1. For every HD value, we maintain a list of nodes in a vector (” that will store information of current node horizontal distance and key value of root “).we also maintain the order of node (order in which they appear in path from root to leaf). for maintaining the order,here we used vector.
2) While we reach to leaf node during traverse we print that path with underscore “_”
Print_Path_with_underscore function 

……a) First find the minimum Horizontal distance of the current path.
……b) After that we traverse current path
……….First Print number of underscore “_” : abs (current_node_HD – minimum-HD)
……….Print current node value.

// store path information

struct PATH

{

    int  Hd; // horigontal distance of node from root.

    char key; // store key

};

 

// Prints given root to leaf path with underscores

void printPath(vector < PATH > path, int size)

{

    // Find the minimum horizontal distance value

    // in current root to leaf path

    int minimum_Hd = INT_MAX;

 

    PATH p;

 

    // find minimum horizontal distance

    for (int it=0; it<size; it++)

    {

        p = path[it];

        minimum_Hd = min(minimum_Hd, p.Hd);

    }

 

    // print the root to leaf path with "_"

    // that indicate the related position

    for (int it=0; it < size; it++)

    {

        // current tree node

        p = path[it];

        int noOfUnderScores = abs(p.Hd - minimum_Hd);

 

        // print underscore

        for (int i = 0; i < noOfUnderScores; i++)

            cout << "_ ";

 

        // print current key

        cout << p.key << endl;

    }

    cout << "==============================" << endl;

}

 

// a utility function print all path from root to leaf

// working of this function is similar to function of

// "Print_vertical_order" : Print paths of binary tree

// in vertical order

// http://www.geeksforgeeks.org/print-binary-tree-vertical-order-set-2/

void printAllPathsUtil(Node *root,

                       vector < PATH > &AllPath,

                       int HD, int order )

{

    // base case

    if(root == NULL)

        return;

 

    // leaf node

    if (root->left == NULL && root->right == NULL)

    {

        // add leaf node and then print path

        AllPath[order] = (PATH { HD, root->data });

        printPath(AllPath, order+1);

        return;

    }

 

    // store current path information

    AllPath[order] = (PATH { HD, root->data });

 

    // call left sub_tree

    printAllPathsUtil(root->left, AllPath, HD-1, order+1);

 

    //call left sub_tree

    printAllPathsUtil(root->right, AllPath, HD+1, order+1);

}

 

void printAllPaths(Node *root)

{

    // base case

    if (root == NULL)

        return;

 

    vector<PATH> Allpaths(MAX_PATH_SIZE);

    printAllPathsUtil(root, Allpaths, 0, 0);

}